Results from an interlaboratory evaluation are said to be statistically consistent if they fit a normal (Gaussian) consistency model which postulates that the results have the same unknown expected value and stated variances and covariances. We propose the use of Bayesian posterior predictive checking to check the fit of the normal consistency model to interlaboratory results. If the model fits, then the results may be regarded as consistent. We discuss a general measure of discrepancy for checking the consistency of interlaboratory results. We also discuss two sets of unilateral and bilateral measures of discrepancy. The degree of agreement is quantified by the Bayesian posterior predictive p-value of discrepancy measures. We suggest that the posterior predicative p-values may be used to define the degrees of equivalence in International Committee of Weights and Measures (CIPM) key comparisons.